Question

Two sides of a triangle measure 11 and 3. Identify the side measure that would not create a triangle
Options
13
Nine
Seven
12

Answer 1

To determine which side measure would not create a triangle with the given two sides (11 and 3), we can use the triangle inequality theorem.

The triangle inequality theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must hold:
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let’s denote the two sides as \(a = 11\) and \(b = 3\). We will check each option to see if it can serve as the third side \(c\).

1. **Option 13**:
- \(11 + 3 > 13\) → \(14 > 13\) (True)
- \(11 + 13 > 3\) → \(24 > 3\) (True)
- \(3 + 13 > 11\) → \(16 > 11\) (True)
- **Valid side**.

2. **Option 9**:
- \(11 + 3 > 9\) → \(14 > 9\) (True)
- \(11 + 9 > 3\) → \(20 > 3\) (True)
- \(3 + 9 > 11\) → \(12 > 11\) (True)
- **Valid side**.

3. **Option 7**:
- \(11 + 3 > 7\) → \(14 > 7\) (True)
- \(11 + 7 > 3\) → \(18 > 3\) (True)
- \(3 + 7 > 11\) → \(10 > 11\) (False)
- **Not a valid side**.

4. **Option 12**:
- \(11 + 3 > 12\) → \(14 > 12\) (True)
- \(11 + 12 > 3\) → \(23 > 3\) (True)
- \(3 + 12 > 11\) → \(15 > 11\) (True)
- **Valid side**.

From the evaluation, the side measure that would not create a triangle is **7**.